Is $(\sin 48)/2$ the same as $\sin 24$? Does $(\sin 48)/2$ simplify to $\sin 24$? I appreciate the fact the sine graph is curved, so would this mean that you could not simply divide the $48$ on the end to receive the correct answer.
$\endgroup$ 43 Answers
$\begingroup$They're different because $(\sin 48)/2 = \sin 24 \cos 24 \neq \sin 24$.
$\endgroup$ 3 $\begingroup$Is ${\sin\pi\over 2}=\sin{\pi\over2}$? Is $0=1?$
$\endgroup$ $\begingroup$You cannot treat the argument of the sin function as a number you can manipulate with constants outside of the scope of $\sin$.
However, since $\sin(2a) = 2\sin a \cos a$, we have $$\dfrac{\sin(48)}2 = \dfrac{\sin (2(24))}2 = \dfrac{2\sin(24)\cos(24)} 2 = \sin (24)\cos (24)$$
$\endgroup$
